Multipath suppression method based on steepest descent method

ABSTRACT

A multipath suppression method based on a steepest descent method includes stripping, according to carrier Doppler shift information fed back by a phase-locked loop, a carrier from an intermediate-frequency signal input into a tracking loop; constructing, on the basis of the autocorrelation characteristics of a ranging code, a quadratic cost function related to a measurement deviation of the ranging code, the cost function being not affected by a multipath signal; and finally, designing a new tracking loop of the ranging code according to the quadratic cost function and the principle of the steepest descent method, such that the loop has a multipath suppression function without increasing the computational burden. Compared with a narrow-distance correlation method, the current method reduces computing resources by ⅓, the design and adjustment of parameters are simple and feasible, a multipath suppression effect is superior, and a high engineering application value is obtained.

RELATED APPLICATIONS

The present application is a U.S. National Phase of InternationalApplication Number PCT/CN2021/105414, filed Jul. 9, 2021, and claimspriority to Chinese Application Number 202010830476.3, filed Aug. 18,2020.

TECHNICAL FIELD

The present disclosure relates to a multipath suppression method basedon a steepest descent method, and belongs to the technical field ofbaseband signal processing.

BACKGROUND

Multipath suppression technology has wide applications in many fields,which get wider with the development of satellite navigation andpositioning technology. In various important application scenarios suchas in a city and on the sea surface, the accuracy of the satellitenavigation and positioning technology is sharply decreased due to thelimitation of the intensive multipath effect, while the multipathsuppression technology can obviously improve the accuracy of thesatellite navigation and positioning.

The current multipath suppression method can be roughly divided intofour types. The first type is to keep away from signal reflectionsources. These methods have been successfully applied to the siteselection and design of an airport, which has a significant suppressioneffect on the multipath, but has a great limitation on the applicationscenarios of receiving machines. The second type is to choose amultipath suppression antenna, such as a choke ring antenna, a blockingplate, a right-handed polarized antenna, a composite antenna, and thelike. These methods require an antenna with a complex design, and theantenna is expensive and has a large volume. The third type is Datapost-processing, such as wavelet transform, carrier phase smoothing,Bayesian estimation, satellite selection. These methods have theproblems of the scenario specificality or huge computation loads. Thefourth type is to improve the structure of the tracking loop, such as,the Narrow-spacing correlation method, Multipath Estimation Delay LockLoop (MEDLL) and Multipath Eliminating Technology (MET). These methodsoccupy a large amount of computation resources.

SUMMARY

Technical problems to be addressed in the present disclosure are toprovide a multipath suppression method based on a steepest descentmethod, which is designed according to peak positions in the X-axis of aranging code autocorrelation function does not move with theNon-Line-of-Sight (NLOS) interference, and is intended to improve aresponse speed of a loop, suppress the multipath effect and reducecomputation loads.

In order to solve the above technical problems, the following technicalsolutions of the present disclosure are adopted.

Provided is a multipath suppression method based on a steepest descentmethod, including the following steps.

In Step 1, according to carrier Doppler shift information fed back by aphase-locked loop, a pair of orthogonal signals are generated by a localcarrier Numerical Controlled Oscillator, and the pair of orthogonalsignals are mixed with an intermediate-frequency signal x(n) input intoa tracking loop of ranging codes respectively, to obtain a pair oforthogonal signals i(n) and q(n) after carrier extracting.

In Step 2, a quadratic cost function PF(R)=(1−R)² is designed, where Rrepresents an autocorrelation function of the ranging codes. Accordingto the quadratic cost function and a principle of the steepest descentmethod, when a right partial derivative of the cost function is adoptedin the control process of a code loop controller, a local punctual codesequence C′(n) and a local early code sequence C′(n+d) are generated bya local ranging-code generator. The orthogonal signals i(n) and q(n) aretaken respectively with the local punctual code sequence C′(n) for acorrelating operation to obtain i_(P)(n) and q_(P)(n), and theorthogonal signals i(n) and q(n) are taken respectively with the localearly code sequence C′(n+d) for a correlating operation to obtaini_(E)(n) and q_(E)(n).

Alternatively, when a left partial derivative of the cost function isadopted in the control process of the code loop controller, the localpunctual-code sequence C′(n) and a local late code sequence C′(n-d) aregenerated by the local ranging-code generator. The orthogonal signalsi(n) and q(n) are taken respectively with the local punctual-codesequence C′(n) for a correlating operation to obtain i_(P)(n) andq_(P)(n), and the orthogonal signals i(n) and q(n) are takenrespectively with the late code sequence C′(n-d) for a correlatingoperation to obtain i_(L)(n) and q_(L)(n); where i_(P)(n) is an I branchsequence correlated with a local punctual code, q_(P)(n) is a Q branchsequence correlated with the local punctual code, i_(L)(n) is an Ibranch sequence correlated with a local late code, q_(L)(n) is a Qbranch sequence correlated with the local late code, i_(E)(n) is an Ibranch sequence correlated with the local early code, and q_(E)(n) is aQ branch sequence correlated with the local early code.

In Step 3, the sequences i_(E)(n), i_(P)(n), q_(E)(n) and q_(P)(n)obtained in Step 2 are taken for a mean-value operation respectively toobtain corresponding I_(E), I_(P), Q_(E) and Q_(P), where I_(E) is amean value of the sequence i_(E)(n); I_(P) is a mean value of thesequence i_(P)(n), Q_(E) is a mean value of the sequence q_(E)(n); andQ_(P) is a mean value of the sequence q_(P)(n).

Alternatively, the sequences i_(L)(n), i_(P)(n), q_(L)(n) and q_(P)(n)obtained in Step 2 are taken for a mean-value operation respectively toobtain corresponding I_(L), I_(P), Q_(L) and Q_(P), where I_(L) is amean value of the sequence i_(L)(n); and Q_(L) is a mean value of thesequence q_(L)(n).

In Step 4, according to the I_(E), I_(P), Q_(E) and Q_(P) obtained inStep 3, a ranging-code offset is calculated by the code loop controllerbased on the steepest descent method, and the ranging code offset is fedback to the local ranging-code generator.

Alternatively, according to the I_(L), I_(P), Q_(L) and Q_(P) obtainedin Step 3, a ranging code offset is calculated by the code loopcontroller based on the steepest descent method, and the ranging codeoffset is fed back to the local ranging-code generator.

As an optimal solution of the present disclosure, the pair of orthogonalsignals are generated by the local carrier Numerical ControlledOscillator, and the pair of orthogonal signals are mixed with theintermediate-frequency signal x(n) input into the tracking loop of theranging codes respectively, to obtain the pair of orthogonal signalsi(n) and q(n) after the carrier extracting, in which the equations areas follows:

$\begin{matrix}{{i(n)} = {{\left( {x(n)} \right)\left( {2{\cos\left( {{w_{I}^{\prime}n} + \theta_{1}} \right)}} \right)} = {{{{AC}(n)}{D(n)}{\cos\left( {\theta_{0} - \theta_{1}} \right)}} + {{AC}(n){D(n)}{\cos\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}} \\{{q(n)} = {{\left( {x(n)} \right)\left( {2{\sin\left( {{w_{I}^{\prime}n} + \theta_{1}} \right)}} \right)} = {{{- {{AC}(n)}}{D(n)}{\sin\left( {\theta_{0} - \theta_{1}} \right)}} + {{AC}(n){D(n)}{\sin\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}}\end{matrix},$where A represents an amplitude of the intermediate-frequency signalx(n) input into the tracking loop, C(n) represents a ranging-codesequence modulated in the intermediate-frequency signal x(n) input intothe tracking loop, D(n) represents a data-code sequence modulated in theintermediate-frequency signal x(n) input into the tracking loop, w′_(I)is an angular velocity of a locally-generated signal, w_(I) representsan intermediate-frequency angular velocity of the intermediate-frequencysignal x(n) input into the tracking loop, where w_(I)−w_(I)≈0, θ₀represents an initial phase of a carrier of the intermediate-frequencysignal x(n) input into the tracking loop, θ₁ represents an initial phaseof a locally-generated carrier signal, and n represents a time point,and an interval between the time point n and a time point n+1 is onesampling period.

As an optimal solution of the present disclosure, as described in Step2, the orthogonal signals i(n) and q(n) are taken respectively with thelocal punctual-code sequence C′(n) for a correlating operation to obtaini_(P)(n) and q_(P)(n), and the orthogonal signals i(n) and q(n) aretaken respectively with the local early code sequence C′(n+d) for acorrelating operation to obtain i_(E)(n) and q_(E)(n), in which theequations are as follows:

$\begin{matrix}{{i_{E}(n)} = {{{i(n)}{C^{\prime}\left( {n + d} \right)}} = {{{{AR}\left( {\overset{\hat{}}{\tau} + d} \right)}{D(n)}{\cos\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( {\overset{\hat{}}{\tau} + d} \right)}{D(n)}{\cos\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}} \\{{i_{P}(n)} = {{{i(n)}{C^{\prime}(n)}} = {{{{AR}\left( \overset{\hat{}}{\tau} \right)}{D(n)}{\cos\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( \overset{\hat{}}{\tau} \right)}{D(n)}{\cos\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}} \\{{q_{E}(n)} = {{{q(n)}{C^{\prime}\left( {n + d} \right)}} = {{{- {{AR}\left( {\overset{\hat{}}{\tau} + d} \right)}}{D(n)}{\sin\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( {\overset{\hat{}}{\tau} + d} \right)}{D(n)}{\sin\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}} \\{{q_{P}(n)} = {{{q(n)}{C^{\prime}(n)}} = {{{- {{AR}\left( \overset{\hat{}}{\tau} \right)}}{D(n)}{\sin\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( \overset{\hat{}}{\tau} \right)}{D(n)}{\sin\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}}\end{matrix}.$

The orthogonal signals i(n) and q(n) are taken respectively with thelocal punctual-code sequence C′(n) for a correlating operation to obtaini_(P)(n) and q_(P)(n), and the orthogonal signals i(n) and q(n) aretaken respectively with the late code sequence C′(n-d) for a correlatingoperation to obtain i_(L)(n) and q_(L)(n), in which the equations are asfollows:

$\begin{matrix}{{i_{L}(n)} = {{{i(n)}{C^{\prime}\left( {n - d} \right)}} = {{{{AR}\left( {\overset{\hat{}}{\tau} - d} \right)}{D(n)}{\cos\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( {\overset{\hat{}}{\tau} - d} \right)}{D(n)}{\cos\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}} \\{{i_{P}(n)} = {{{i(n)}{C^{\prime}(n)}} = {{{{AR}\left( \overset{\hat{}}{\tau} \right)}{D(n)}{\cos\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( \overset{\hat{}}{\tau} \right)}{D(n)}{\cos\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}} \\{{q_{L}(n)} = {{{q(n)}{C^{\prime}\left( {n - d} \right)}} = {{{- {{AR}\left( {\overset{\hat{}}{\tau} - d} \right)}}{D(n)}{\sin\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( {\overset{\hat{}}{\tau} - d} \right)}{D(n)}{\sin\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}} \\{{q_{P}(n)} = {{{q(n)}{C^{\prime}(n)}} = {{{- {{AR}\left( \overset{\hat{}}{\tau} \right)}}{D(n)}{\sin\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( \overset{\hat{}}{\tau} \right)}{D(n)}{\sin\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}}\end{matrix}.$where A represents an amplitude of the intermediate-frequency signalx(n) input into the tracking loop, D(n) represents a data-code sequencemodulated in the intermediate-frequency signal x(n) input into thetracking loop, w_(I) represents an intermediate-frequency angularvelocity of the intermediate-frequency signal x(n) input into thetracking loop, θ₀ represents an initial phase of a carrier of theintermediate-frequency signal x(n) input into the tracking loop; θ₁represents an initial phase of a locally-generated carrier signal; nrepresents a time point, R(·) represents an autocorrelation function ofranging codes, {circumflex over (τ)} represents a distance between thelocal punctual code and a signal ranging code, and d represents aninterval of the ranging codes.

As an optimal solution of the present disclosure, the equations of theI_(E), I_(P), Q_(E) and Q_(P) as described in Step 3 are as follows:

$\begin{matrix}{I_{E} = {{\frac{1}{{Tf}_{s}}{\sum\limits_{n = 1}^{{Tf}_{s}}{i_{E}(n)}}} \approx {AR\left( {\overset{\hat{}}{\tau} + d} \right)\cos\left( {\theta_{0} - \theta_{1}} \right)}}} \\{I_{P} = {{\frac{1}{{Tf}_{s}}{\sum\limits_{n = 1}^{{Tf}_{s}}{i_{P}(n)}}} \approx {AR\left( \overset{\hat{}}{\tau} \right)\cos\left( {\theta_{0} - \theta_{1}} \right)}}} \\{Q_{E} = {{\frac{1}{{Tf}_{s}}{\sum\limits_{n = 1}^{{Tf}_{s}}{q_{E}(n)}}} \approx {{- {AR}}\left( {\overset{\hat{}}{\tau} + d} \right){\sin\left( {\theta_{0} - \theta_{1}} \right)}}}} \\{Q_{p} = {{\frac{1}{{Tf}_{s}}{\sum\limits_{n = 1}^{{Tf}_{s}}{q_{p}(n)}}} \approx {{- {AR}}\left( \overset{\hat{}}{\tau} \right){\sin\left( {\theta_{0} - \theta_{1}} \right)}}}}\end{matrix}.$the equations of the I_(L), I_(P), Q_(L) and Q_(P) are as follows:

$\begin{matrix}{I_{L} = {{\frac{1}{{Tf}_{s}}{\sum\limits_{n = 1}^{{Tf}_{s}}{i_{L}(n)}}} \approx {AR\left( {\overset{\hat{}}{\tau} - d} \right)\cos\left( {\theta_{0} - \theta_{1}} \right)}}} \\{I_{P} = {{\frac{1}{{Tf}_{s}}{\sum\limits_{n = 1}^{{Tf}_{s}}{i_{P}(n)}}} \approx {AR\left( \overset{\hat{}}{\tau} \right)\cos\left( {\theta_{0} - \theta_{1}} \right)}}} \\{Q_{L} = {{\frac{1}{{Tf}_{s}}{\sum\limits_{n = 1}^{{Tf}_{s}}{q_{L}(n)}}} \approx {{- {AR}}\left( {\overset{\hat{}}{\tau} - d} \right)\sin\left( {\theta_{0} - \theta_{1}} \right)}}} \\{Q_{p} = {{\frac{1}{{Tf}_{s}}{\sum\limits_{n = 1}^{{Tf}_{s}}{q_{p}(n)}}} \approx {{- {AR}}\left( \overset{\hat{}}{\tau} \right)\sin\left( {\theta_{0} - \theta_{1}} \right)}}}\end{matrix},$where T represents an integration time, f_(s) represents a samplingrate, n represents a time point, A represents an amplitude of theintermediate-frequency signal x(n) input into the tracking loop, R(·)represents an autocorrelation function of ranging codes, {circumflexover (τ)} represents a distance between the local punctual code and asignal ranging code, d represents an interval of the ranging codes, θ₀represents an initial phase of a carrier of the intermediate-frequencysignal x(n) input into the tracking loop; and θ₁ represents an initialphase of a locally-generated carrier signal.

As an optimal solution of the present disclosure, the equation of theranging code offset described in Step 4 is as follows:

${{\overset{\hat{}}{\tau}}_{k + 1} = {{\overset{\hat{}}{\tau}}_{k} - {\mu\frac{{P{F\left( {{\overset{¯}{S}}_{E}❘_{k}} \right)}} - {P{F\left( {{\overset{¯}{S}}_{P}❘_{k}} \right)}}}{d}}}},$or the equation is as follows:

${{\overset{\hat{}}{\tau}}_{k + 1} = {{\overset{\hat{}}{\tau}}_{k} - {\mu\frac{{P{F\left( {{\overset{¯}{S}}_{P}❘_{k}} \right)}} - {P{F\left( {{\overset{¯}{S}}_{L}❘_{k}} \right)}}}{d}}}},$where {circumflex over (τ)}_(k+1), and {circumflex over (τ)}_(k)respectively represent {circumflex over (τ)} at a time point k+1 and atime point k, {circumflex over (τ)} represents a distance between thelocal punctual code and a signal ranging code, an interval between thetime point k+1 and the time point k is an integration time, μ is apositive scalar named step length, PF(·) represents a cost function, S_(E)|_(k) S _(P)|_(k) and S _(L)|_(k) respectively represent values of S_(E), S _(P), and S _(L) at the time point k, S _(E) represents anormalized value of S_(E), S _(P) represents a normalized value ofS_(P), S _(L) represents a normalized value of S_(L), andS _(E)=√{square root over (I _(E) ² +Q _(E) ²)},S _(P)=√{square rootover (I _(P) ² +Q _(P) ²)},S _(L)=√{square root over (I _(L) ² +Q _(L)²)}.

Compared to the prior arts, the technical solutions adopted in thepresent disclosure have the following beneficial effects.

1. A multipath suppression mechanism is adopted in the presentdisclosure, and the conclusion from the autocorrelation function of theranging codes can better suppress the multipath effect and realize ashorter adjustment time and a smaller steady-state error for a multipathsuppression loop.

2. Compared with the traditional narrow-distance correlation method, themultipath suppression loop designed in the present disclosure spares onebranch of an advanced branch or a lagging branch, thereby reducing thecomputation loads by nearly ⅓.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a schematic diagram of a multipath suppression loopof the present disclosure.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The embodiments of the present disclosure will be described below indetail, examples of which are illustrated in the drawings. Theembodiments described below in combination with the drawings areexemplary and are merely to explain the present disclosure rather thanbeing interpreted as limitation on the present disclosure.

A multipath suppression loop method based on a steepest descent method,as illustrated in FIG. 1 , including four parts in total. Firstly,carriers are mixed; secondly, the ranging codes are taken forcorrelating operations; then, a process of low-pass filtering isconducted; and eventually, the tracking loop of the ranging codes iscontrolled by the code loop control algorithm designed in the presentdisclosure. The process of the present disclosure is described in detailbelow.

Step 1: Carrier Mixing

According to carrier Doppler-frequency-shift information fed back by aphase-locked loop, a pair of orthogonal signals are generated by a localcarrier Numerical Controlled Oscillator (NCO), and are mixed with anintermediate-frequency signal x(n) input into a tracking looprespectively, to obtain orthogonal sequences i(n) and q(n) after carrierextracting.

Assumed is that the signal structure of the intermediate-frequencysignal input to the tracking loop is shown as the following equation:x(n)=AC(n)D(n)cos(w _(I) n+θ ₀).

In the above equation, A represents an amplitude of theintermediate-frequency signal x(n) input into the tracking loop, C(n)represents a ranging-code sequence modulated in theintermediate-frequency signal x(n) input into the tracking loop, D(n)represents a data-code sequence modulated in the intermediate-frequencysignal x(n) input into the tracking loop, w_(I) represents anintermediate-frequency angular velocity of the intermediate-frequencysignal x(n) input into the tracking loop, θ₀ represents an initial phaseof a carrier of the intermediate-frequency signal x(n) input into thetracking loop.

A pair of orthogonal signals generated by the local carrier NCO aremixed with the x(n) respectively, and a high-frequency component isremoved to obtain a pair of orthogonal signals i(n) and q(n). Theprocess is shown as the following equation:

$\begin{matrix}{{i(n)} = {{\left( {x(n)} \right)\left( {2\cos\left( {{w_{I}^{\prime}n} + \theta_{1}} \right)} \right)} = {{{{AC}(n)}D(n){\cos\left( {\theta_{0} - \theta_{1} + {\left( {w_{I} - w_{I}^{\prime}} \right)n}} \right)}} + {AC(n)D(n)\cos\left( {{\left( {w_{I} + w_{I}^{\prime}} \right)n} + \theta_{0} + \theta_{1}} \right)}}}} \\{{q(n)} = {{\left( {x(n)} \right)\left( {2\sin\left( {{w_{I}^{\prime}n} + \theta_{1}} \right)} \right)} = {{{- {{AC}(n)}}D(n){\sin\left( {\theta_{0} - \theta_{1} + {\left( {w_{I} - w_{I}^{\prime}} \right)n}} \right)}} + {{AC}(n)D(n)\sin\left( {{\left( {w_{I} + w_{I}^{\prime}} \right)n} + \theta_{0} + \theta_{1}} \right)}}}}\end{matrix},$

In the above equation, w′_(I) is an angular velocity of alocally-generated signal, θ₁ represents an initial phase of alocally-generated carrier signal, where w_(I)−w′_(I)≈0 due to thephase-locked-loop feedback. Therefore, the pair of orthogonal signalsi(n) and q(n) obtained after frequency mixing can be simplified as:

$\begin{matrix}{{{i(n)} = {\left( {x(n)} \right)\left( {2\cos\left( {{w_{I}^{\prime}n} + \theta_{1}} \right)} \right)}}{= {{AC(n)D(n)\cos\left( {\theta_{0} - \theta_{1}} \right)} + {AC(n)D(n)\cos\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}} \\{{{q(n)} = {\left( {x(n)} \right)\left( {2\sin\left( {{w_{I}^{\prime}n} + \theta_{1}} \right)} \right)}}{= {{{- {{AC}(n)}}D(n){\sin\left( {\theta_{0} - \theta_{1}} \right)}} + {AC(n)D(n)\sin\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}\end{matrix}.$

Step 2: Correlating Operations of the Ranging Codes

According to the fact that the control process of the code loopcontroller designed in the present disclosure adopts a left partialderivative or a right partial derivative of the cost functionPF({circumflex over (τ)}), two strategies can be adopted by the process,and only one of the two strategies is required to be selected. Two codesequences are generated by a local ranging-code generator. When the leftpartial derivative of the function PF({circumflex over (τ)}) is adopted,the two code sequences are a local punctual-code sequence C′(n) and alocal late code sequence C′(n−d) respectively; and when the rightpartial derivative of the function PF(i) is adopted, the two codesequences are the local punctual-code sequence C′(n) and a local earlycodesequence C′(n+d) respectively.

When the right partial derivative is adopted, the process of the codecorrelating operation is as follows.

The local punctual-code sequence C′(n) with 1 ms duration and the localearly codesequence C′(n+d) with 1 ms duration are taken respectivelywith a pair of orthogonal signals i(n) and q(n) after extracting off thecarrier with 1 ms duration for a correlating operation. The operationprocess is as follows:

$\begin{matrix}{{i_{E}(n)} = {{i(n)C^{\prime}\left( {n + d} \right)} = {{{{AR}\left( {\overset{\hat{}}{\tau} + d} \right)}{D(n)}{\cos\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( {\overset{\hat{}}{\tau} + d} \right)}{D(n)}{\cos\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}} \\{{i_{P}(n)} = {{i(n){C^{\prime}(n)}} = {{{{AR}\left( \overset{\hat{}}{\tau} \right)}{D(n)}{\cos\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( \overset{\hat{}}{\tau} \right)}{D(n)}{\cos\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}} \\{{q_{E}(n)} = {{q(n)C^{\prime}\left( {n + d} \right)} = {{{- {{AR}\left( {\overset{\hat{}}{\tau} + d} \right)}}{D(n)}{\sin\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( {\overset{\hat{}}{\tau} + d} \right)}{D(n)}{\sin\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}} \\{{q_{P}(n)} = {{q(n){C^{\prime}(n)}} = {{{- {{AR}\left( \overset{\hat{}}{\tau} \right)}}{D(n)}{\sin\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( \overset{\hat{}}{\tau} \right)}{D(n)}{\sin\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}}\end{matrix}.$

In the above equations, d represents an interval of the ranging codes,i_(E)(n) is an I branch sequence with 1 ms duration correlated with thelocal early code, i_(P)(n) is an I branch sequence with 1 ms durationcorrelated with the local punctual code, q_(E)(n) is a Q branch sequencewith 1 ms duration correlated with the local early code, and q_(P)(n) isa Q branch sequence with 1 ms duration correlated with the localpunctual code.

When the left partial derivative is adopted, the process of the codecorrelating operation is as follows.

The local punctual-code sequence C′(n) with 1 ms duration and the locallate code sequence C′(n−d) with 1 ms duration are taken respectivelywith a pair of orthogonal signals i(n) and q(n) after extracting off thecarrier with 1 ms duration for a correlating operation. The operationprocess is as follows:

$\begin{matrix}{{i_{L}(n)} = {{i(n)C^{\prime}\left( {n - d} \right)} = {{{{AR}\left( {\overset{\hat{}}{\tau} - d} \right)}{D(n)}{\cos\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( {\overset{\hat{}}{\tau} - d} \right)}{D(n)}{\cos\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}} \\{{i_{P}(n)} = {{i(n){C^{\prime}(n)}} = {{{{AR}\left( \overset{\hat{}}{\tau} \right)}{D(n)}{\cos\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( \overset{\hat{}}{\tau} \right)}{D(n)}{\cos\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}} \\{{q_{L}(n)} = {{q(n)C^{\prime}\left( {n - d} \right)} = {{{- {{AR}\left( {\overset{\hat{}}{\tau} - d} \right)}}{D(n)}{\sin\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( {\overset{\hat{}}{\tau} - d} \right)}{D(n)}{\sin\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}} \\{{q_{P}(n)} = {{q(n){C^{\prime}(n)}} = {{{- {{AR}\left( \overset{\hat{}}{\tau} \right)}}{D(n)}{\sin\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( \overset{\hat{}}{\tau} \right)}{D(n)}{\sin\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}}\end{matrix}.$

In the above equations, d represents the interval of the ranging codes,i_(L)(n) is an I branch sequence with 1 ms duration correlated with thelocal late code, i_(P)(n) is an I branch sequence with 1 ms durationcorrelated with the local punctual code, q_(L)(n) is a Q branch sequencewith 1 ms duration correlated with the local late code, and q_(P)(n) isa Q branch sequence with 1 ms duration correlated with the localpunctual code.

Step 3: Low-Pass Filtering

The sequences i_(E)(n), i_(P)(n), q_(E)(n) and q_(P)(n) with 1 msduration obtained in Step 2 are taken for a mean-value operationrespectively to obtain corresponding four values of I_(E), I_(P), Q_(E)and Q_(P). Alternatively, the sequences i_(L)(n), i_(P)(n), q_(L)(n) andq_(P)(n) with 1 ms duration obtained in Step 2 are taken for amean-value operation respectively to obtain corresponding four values ofI_(L), I_(P), Q_(L) and Q_(P.)

When the right partial derivative is adopted, since the data code D(n)is a constant in the integration period, the signals passing through thelow-pass filtering are shown as the following equations:

$\begin{matrix}{I_{E} = {{\frac{1}{Tf_{s}}{\sum\limits_{n = 1}^{Tf_{s}}{i_{E}(n)}}} \approx {AR\left( {\overset{\hat{}}{\tau} + d} \right)\cos\left( {\theta_{0} - \theta_{1}} \right)}}} \\{I_{P} = {{\frac{1}{Tf_{s}}{\sum\limits_{n = 1}^{Tf_{s}}{i_{P}(n)}}} \approx {AR\left( \overset{\hat{}}{\tau} \right)\cos\left( {\theta_{0} - \theta_{1}} \right)}}} \\{Q_{E} = {{\frac{1}{Tf_{s}}{\sum\limits_{n = 1}^{Tf_{s}}{q_{E}(n)}}} \approx {{- {AR}}\left( {\overset{\hat{}}{\tau} + d} \right)\sin\left( {\theta_{0} - \theta_{1}} \right)}}} \\{Q_{p} = {{\frac{1}{Tf_{s}}{\sum\limits_{n = 1}^{Tf_{s}}{q_{p}(n)}}} \approx {{- {AR}}\left( \overset{\hat{}}{\tau} \right)\sin\left( {\theta_{0} - \theta_{1}} \right)}}}\end{matrix}.$

In the above equations, T represents an integration time which isinteger multiples of a period of a ranging code generally, and is set as1 ms in the present disclosure, f_(s) represents a sampling rate, R(·)represents an autocorrelation function of the ranging codes, {circumflexover (τ)} represents a distance between the local punctual code and asignal ranging code, I_(E) is a mean value of the sequence i_(E)(n),which is a number; I_(P) is a mean value of the sequence i_(P)(n), whichis a number; Q_(E) is a mean value of the sequence q_(E)(n), which is anumber; and Q_(P) is a mean value of the sequence q_(P)(n), which is anumber.

When the left partial derivative is adopted, since the data code D(n) isa constant in the integration period, the signals passing through thelow-pass filtering are shown as the following equations:

$\begin{matrix}{I_{L} = {{\frac{1}{{Tf}_{s}}{\sum\limits_{n = 1}^{Tf_{s}}{i_{L}(n)}}} \approx {AR\left( {\overset{\hat{}}{\tau} - d} \right)\cos\left( {\theta_{0} - \theta_{1}} \right)}}} \\{I_{P} = {{\frac{1}{{Tf}_{s}}{\sum\limits_{n = 1}^{Tf_{s}}{i_{P}(n)}}} \approx {AR\left( \overset{\hat{}}{\tau} \right)\cos\left( {\theta_{0} - \theta_{1}} \right)}}} \\{Q_{L} = {{\frac{1}{{Tf}_{s}}{\sum\limits_{n = 1}^{Tf_{s}}{q_{L}(n)}}} \approx {{- {AR}}\left( {\overset{\hat{}}{\tau} - d} \right)\sin\left( {\theta_{0} - \theta_{1}} \right)}}} \\{Q_{p} = {{\frac{1}{{Tf}_{s}}{\sum\limits_{n = 1}^{Tf_{s}}{q_{p}(n)}}} \approx {{- {AR}}\left( \overset{\hat{}}{\tau} \right)\sin\left( {\theta_{0} - \theta_{1}} \right)}}}\end{matrix}.$

In the above equations, T represents an integration time which isinteger multiples of a period of a ranging code generally, and is set as1 ms in the present disclosure, f_(s) represents a sampling rate, R(·)represents an autocorrelation function of the ranging codes, {circumflexover (τ)} represents a distance between the local punctual code and asignal ranging code, I_(L) is a mean value of the sequence i_(L)(n),which is a number; I_(P) is a mean value of the sequence i_(P)(n), whichis a number; Q_(L) is a mean value of the sequence q_(L)(n), which is anumber; and Q_(P) is a mean value of the sequence q_(P)(n), which is anumber.

Step 4: Code Loop Control

According to the I_(E), I_(P), Q_(E) and Q_(P) obtained in Step 3, aranging code offset is calculated by the code loop controller based onthe steepest descent method, and the ranging code offset is fed back tothe local ranging-code generator. Alternatively, according to the I_(L),I_(P), Q_(L) and Q_(P) obtained in Step 3, a ranging code offset iscalculated by the code loop controller based on the steepest descentmethod, and the ranging code offset is fed back to the localranging-code generator.

The following describes the principle of the code loop controller basedon the steepest descent method.

Firstly, according to an autocorrelation function of the ranging codes,a cost function is defined as follows: PF(R)=(1−R)².

The I_(E), I_(P), Q_(E) and Q_(P) obtained in Step 3 involve carrierinformation. In order to weaken the influence of the carrier on the codeloop control process, the values are required to be processed under thefollowing equations:S _(E)√{square root over (I _(E) ² +Q _(E) ²)}=AR({circumflex over(τ)}+d)S _(P)=√{square root over (I _(P) ² +Q _(P) ²)}=AR({circumflex over(τ)})

In the above equations, S_(E) represents a correlation value of theearly code, which is a numerical value; and S_(P) represents acorrelation value of the punctual code, which is a numerical value.

Since the amplitude of the signal x(n) is a constant in a short time,and the maximum value of the autocorrelation function RO of the rangingcodes is 1, the influence of the amplitude A on the correlation peakscan be eliminated by signal normalization. The normalization process isshown in the following equations:S _(E) =S _(E) /S _(max) ≈R({circumflex over (τ)}+d)S _(P) =S _(P) /S _(max) ≈R({circumflex over (τ)})

In the above equations, S_(max) represents a larger value between themaximum value of S_(E) and the maximum value of S_(P) in the trackingprocess, and S _(E) represents a normalized early-code correlationvalue, and S _(P) represents a normalized punctual-code correlationvalue.

Through the above analysis, the values of the cost function for S _(E)and S _(P) can be obtained, as shown in the following equations:PF( S _(E))=(1− S _(E))²PF( S _(P))=(1− S _(P))²

According to the principle of the steepest descent method, thecontrolling equation of the distance between the locally-generatedpunctual code and a signal ranging code can be obtained by using theright partial derivative of the functions, as shown in the followingequation:

${\overset{\hat{}}{\tau}}_{k + 1} = {{\overset{\hat{}}{\tau}}_{k} - {\mu{\frac{{P{F\left( {{\overset{¯}{S}}_{E}❘_{k}} \right)}} - {P{F\left( {{\overset{¯}{S}}_{P}❘_{k}} \right)}}}{d}.}}}$

In the above equation, μ is a positive scalar named step length,{circumflex over (τ)}_(k) represents a distance between the localpunctual code and the signal ranging code in the current second,{circumflex over (τ)}_(k+1) represents a distance between the localpunctual code and the signal ranging code in the next second, PF(S_(E)|_(k)) represents a value of the cost function for a normalizedearly-code correlation value in the current second, and PF(S _(P)|_(K))represents a value of the cost function for a normalized punctual-codecorrelation value in the current second.

Alternatively, the I_(L), I_(P), Q_(L) and Q_(P) obtained in Step 3involve carrier information. In order to weaken the influence of thecarrier on the code loop control process, the values are required to beprocessed under the following equations:S _(L)=√{square root over (I _(L) ² +Q _(L) ²)}=AR({circumflex over(τ)}−d)S _(P)=√{square root over (I _(P) ² +Q _(P) ²)}=AR({circumflex over(τ)})

In the above equations, S_(L) represents a correlation value of the latecode, which is a numerical value; and S_(P) represents a correlationvalue of the punctual code, which is a numerical value.

Since the amplitude of the signal x(n) is a constant in a short time,and the maximum value of the autocorrelation function RO of the rangingcodes is 1, the influence of the amplitude A on the correlation peak canbe eliminated by the signal normalization. The normalization process isshown as the following equations:S _(L) =S _(L) |S _(max) ≈R({circumflex over (τ)}−d)S _(P) =S _(P) |S _(max) ≈R({circumflex over (τ)})

In the above equations, S_(max) represents a larger value between themaximum value of S_(L) and the maximum value of S_(P) in the trackingprocess, and S _(L) represents a normalized late code correlation value,and S _(P) represents a normalized punctual-code correlation value.

Through the above analysis, the value of the cost function for S _(L)and S _(P) can be obtained, as shown in the following equations:PF( S _(L))=(1− S _(L))²PF( S _(P))=(1− S _(P))²

According to the principle of the steepest descent method, thecontrolling equation of the distance between the locally generatedpunctual code and a signal ranging code can be obtained by using theright partial derivative of the function, as shown in the followingequation:

${\overset{\hat{}}{\tau}}_{k + 1} = {{\overset{\hat{}}{\tau}}_{k} - {\mu{\frac{\left. {{{P{F\left( {{\overset{¯}{S}}_{P}❘_{k}} \right)}} - {P{F\left( {\overset{¯}{S}}_{L} \right.}}}❘}_{k} \right)}{d}.}}}$

In the above equation, ρ is a positive scalar named step length,{circumflex over (τ)}_(k) represents a distance between the localpunctual code and the signal ranging code in the current second,{circumflex over (τ)}_(k+1) represents a distance between the localpunctual code and the signal ranging code in the next second, PF(S_(L)|_(K)) represents a value of the cost function for a normalized latecode correlation value in the current second, and PF(S_(P)|_(K))represents a value of the cost function for a normalized punctual-codecorrelation value in the current second.

The above embodiments are only to illustrate the technical spirits ofthe present disclosure and cannot be used to limit the protection scopeof the present disclosure. Any changes made on the basis of thetechnical scheme in accordance with the technical spirits of the presentdisclosure shall fall within the protection scope of the presentdisclosure.

What is claimed is:
 1. A multipath suppression method based on asteepest descent method, comprising following steps: Step 1, generating,according to carrier Doppler-frequency-shift information fed back by aphase-locked loop, a pair of orthogonal signals by a local carrierNumerical Controlled Oscillator, and mixing the pair of orthogonalsignals with an intermediate-frequency signal x(n) input into a trackingloop of ranging codes respectively, to obtain a pair of orthogonalsignals i(n) and q(n) after carrier extracting; Step 2, designing, aquadratic cost function PF(R)=(1−R)², where R represents anautocorrelation function of the ranging codes, according to thequadratic cost function and a principle of the steepest descent method,when a right partial derivative of the cost function is adopted in acontrol process of a code loop controller, a local punctual-codesequence C′(n) and a local early codesequence C′(n+d) are generated by alocal ranging-code generator, and the orthogonal signals i(n) and q(n)are taken respectively with the local punctual-code sequence C′(n) for acorrelating operation to obtain i_(P)(n) and q_(P)(n), and theorthogonal signals i(n) and q(n) are taken respectively with the localearly codesequence C′(n+d) for a correlating operation to obtaini_(E)(n) and q_(E)(n); or when a left partial derivative of the costfunction is adopted in a control process of a code loop controller, alocal punctual-code sequence C′(n) and a local late code sequenceC′(n-d) are generated by a local ranging-code generator, and theorthogonal signals i(n) and q(n) are taken respectively with the localpunctual-code sequence C′(n) for a correlating operation to obtaini_(P)(n) and q_(P)(n), and the orthogonal signals i(n) and q(n) aretaken respectively with the late code sequence C′(n−d) of a correlatingoperation to obtain i_(L)(n) and q_(L)(n); where i_(P)(n) is an I branchsequence correlated with a local punctual code, q_(P)(n) is a Q branchsequence correlated with the local punctual code, i_(L)(n) is an Ibranch sequence correlated with a local late code, q_(L)(n) is a Qbranch sequence correlated with the local late code, i_(E)(n) is an Ibranch sequence correlated with a local early code, and q_(E)(n) is a Qbranch sequence correlated with the local early code; Step 3, taking thesequences i_(E)(n), i_(P)(n), q_(E)(n) and q_(P)(n) obtained in Step 2for a mean-value operation respectively to obtain corresponding I_(E),I_(P), Q_(E) and Q_(P), where I_(E) is a mean value of the sequencei_(E)(n); I_(P) is a mean value of the sequence i_(P)(n), Q_(E) is amean value of the sequence q_(E)(n); and Q_(P) is a mean value of thesequence q_(P)(n); or taking the sequences i_(L)(n), i_(P)(n), q_(L)(n)and q_(P)(n) obtained in Step 2 for a mean-value operation respectivelyto obtain corresponding I_(L), I_(P), Q_(L) and Q_(P), where I_(L) is amean value of the sequence i_(L)(n); Q_(L) is a mean value of thesequence q_(L)(n); and Step 4, calculating, according to the I_(E),I_(P), Q_(E) and Q_(P) obtained in Step 3, a ranging code offset by thecode loop controller based on the steepest descent method, and feedingthe ranging code offset back to the local ranging-code generator; orcalculating, according to the I_(L), I_(P), Q_(L) and Q_(P) obtained inStep 3, a ranging code offset through the code loop controller based onthe steepest descent method, and feeding the ranging code offset back tothe local ranging-code generator.
 2. The multipath suppression methodbased on the steepest descent method according to claim 1, wherein inthe generating, the pair of orthogonal signals by the local carrierNumerical Controlled Oscillator, and mixing the pair of orthogonalsignals with the intermediate-frequency signal x(n) input into thetracking loop of the ranging codes respectively, to obtain the pair oforthogonal signals i(n) and q(n) after the carrier extracting, equationsare as follows: $\begin{matrix}{{i(n)} = {{\left( {x(n)} \right)\left( {2\cos\left( {{w_{I}^{\prime}n} + \theta_{1}} \right)} \right)} = {{{{AC}(n)}{D(n)}{\cos\left( {\theta_{0} - \theta_{1}} \right)}} + {A{C(n)}{D(n)}{\cos\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}} \\{{q(n)} = {{\left( {x(n)} \right)\left( {2\sin\left( {{w_{I}^{\prime}n} + \theta_{1}} \right)} \right)} = {{{- {{AC}(n)}}{D(n)}{\sin\left( {\theta_{0} - \theta_{1}} \right)}} + {A{C(n)}{D(n)}{\sin\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}}\end{matrix},$ where A represents an amplitude of theintermediate-frequency signal x(n) input into the tracking loop; C(n)represents a ranging-code sequence modulated in theintermediate-frequency signal x(n) input into the tracking loop; D(n)represents a data-code sequence modulated in the intermediate-frequencysignal x(n) input into the tracking loop; w′_(I) is an angular velocityof a locally-generated signal; w_(I) represents anintermediate-frequency angular velocity of the intermediate-frequencysignal x(n) input into the tracking loop, where w_(I)−w′_(I)≈0; θ₀represents an initial phase of a carrier of the intermediate-frequencysignal x(n) input into the tracking loop; θ₁ represents an initial phaseof a locally-generated carrier signal; n represents a time point, and aninterval between the time point n and a time point n+1 is one samplingperiod.
 3. The multipath suppression method based on the steepestdescent method according to claim 1, wherein, in Step 2, in the takingthe orthogonal signals i(n) and q(n) respectively with the localpunctual-code sequence C′(n) for the correlating operation to obtaini_(P)(n) and q_(P)(n), and taking the orthogonal signals i(n) and q(n)respectively with the local early codesequence C′(n+d) for thecorrelating operation to obtain i_(E)(n) and q_(E)(n), equations are asfollows: $\begin{matrix}{{i_{E}(n)} = {{i(n)C^{\prime}\left( {n + d} \right)} = {{{{AR}\left( {\overset{\hat{}}{\tau} + d} \right)}{D(n)}{\cos\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( {\overset{\hat{}}{\tau} + d} \right)}{D(n)}{\cos\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}} \\{{i_{P}(n)} = {{i(n){C^{\prime}(n)}} = {{{{AR}\left( \overset{\hat{}}{\tau} \right)}{D(n)}{\cos\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( \overset{\hat{}}{\tau} \right)}{D(n)}{\cos\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}} \\{{q_{E}(n)} = {{q(n)C^{\prime}\left( {n + d} \right)} = {{{- {{AR}\left( {\overset{\hat{}}{\tau} + d} \right)}}{D(n)}{\sin\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( {\overset{\hat{}}{\tau} + d} \right)}{D(n)}{\sin\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}} \\{{q_{P}(n)} = {{q(n){C^{\prime}(n)}} = {{{- {{AR}\left( \overset{\hat{}}{\tau} \right)}}{D(n)}{\sin\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( \overset{\hat{}}{\tau} \right)}{D(n)}{\sin\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}}\end{matrix},$ in the taking the orthogonal signals i(n) and q(n)respectively with the local punctual-code sequence C′(n) for thecorrelating operation to obtain i_(P)(n) and q_(P)(n), and taking theorthogonal signals i(n) and q(n) respectively with the late codesequence C′(n-d) for the correlating operation to obtain i_(L)(n) andq_(L)(n), equations are as follows: $\begin{matrix}{{i_{L}(n)} = {{i(n)C^{\prime}\left( {n - d} \right)} = {{{{AR}\left( {\overset{\hat{}}{\tau} - d} \right)}{D(n)}{\cos\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( {\overset{\hat{}}{\tau} - d} \right)}{D(n)}{\cos\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}} \\{{i_{P}(n)} = {{i(n){C^{\prime}(n)}} = {{{{AR}\left( \overset{\hat{}}{\tau} \right)}{D(n)}{\cos\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( \overset{\hat{}}{\tau} \right)}{D(n)}{\cos\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}} \\{{q_{L}(n)} = {{q(n)C^{\prime}\left( {n - d} \right)} = {{{- {{AR}\left( {\overset{\hat{}}{\tau} - d} \right)}}{D(n)}{\sin\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( {\overset{\hat{}}{\tau} - d} \right)}{D(n)}{\sin\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}} \\{{q_{P}(n)} = {{q(n){C^{\prime}(n)}} = {{{- {{AR}\left( \overset{\hat{}}{\tau} \right)}}{D(n)}{\sin\left( {\theta_{0} - \theta_{1}} \right)}} + {A{R\left( \overset{\hat{}}{\tau} \right)}{D(n)}{\sin\left( {{2w_{I}n} + \theta_{0} + \theta_{1}} \right)}}}}}\end{matrix},$ where A represents an amplitude of theintermediate-frequency signal x(n) input into the tracking loop, D(n)represents a data-code sequence modulated in the intermediate-frequencysignal x(n) input into the tracking loop, w_(I) represents anintermediate-frequency angular velocity of the intermediate-frequencysignal x(n) input into the tracking loop, θ₀ represents an initial phaseof a carrier of the intermediate-frequency signal x(n) input into thetracking loop; θ₁ represents an initial phase of a locally-generatedcarrier signal; {circumflex over (τ)} represents a time point, R(·)represents an autocorrelation function of the ranging codes, {circumflexover (τ)} represents a distance between the local punctual code and asignal ranging code, and d represents an interval of the ranging codes.4. The multipath suppression method based on the steepest descent methodaccording to claim 1, wherein equations of the I_(E), I_(P), Q_(E) andQ_(P) in Step 3 are as follows: $\begin{matrix}{I_{E} = {{\frac{1}{{Tf}_{s}}{\sum\limits_{n = 1}^{{Tf}_{s}}{i_{E}(n)}}} \approx {AR\left( {\overset{\hat{}}{\tau} + d} \right)\cos\left( {\theta_{0} - \theta_{1}} \right)}}} \\{I_{P} = {{\frac{1}{{Tf}_{s}}{\sum\limits_{n = 1}^{{Tf}_{s}}{i_{P}(n)}}} \approx {AR\left( \overset{\hat{}}{\tau} \right)\cos\left( {\theta_{0} - \theta_{1}} \right)}}} \\{Q_{E} = {{\frac{1}{{Tf}_{s}}{\sum\limits_{n = 1}^{{Tf}_{s}}{q_{E}(n)}}} \approx {{- {AR}}\left( {\overset{\hat{}}{\tau} + d} \right){\sin\left( {\theta_{0} - \theta_{1}} \right)}}}} \\{Q_{p} = {{\frac{1}{{Tf}_{s}}{\sum\limits_{n = 1}^{{Tf}_{s}}{q_{p}(n)}}} \approx {{- {AR}}\left( \overset{\hat{}}{\tau} \right){\sin\left( {\theta_{0} - \theta_{1}} \right)}}}}\end{matrix},{and}$ equations of the I_(L), I_(P), Q_(L) and Q_(P) areas follows: $\begin{matrix}{I_{L} = {{\frac{1}{{Tf}_{s}}{\sum\limits_{n = 1}^{{Tf}_{s}}{i_{L}(n)}}} \approx {AR\left( {\overset{\hat{}}{\tau} - d} \right)\cos\left( {\theta_{0} - \theta_{1}} \right)}}} \\{I_{P} = {{\frac{1}{{Tf}_{s}}{\sum\limits_{n = 1}^{{Tf}_{s}}{i_{P}(n)}}} \approx {AR\left( \overset{\hat{}}{\tau} \right)\cos\left( {\theta_{0} - \theta_{1}} \right)}}} \\{Q_{L} = {{\frac{1}{{Tf}_{s}}{\sum\limits_{n = 1}^{{Tf}_{s}}{q_{L}(n)}}} \approx {{- {AR}}\left( {\overset{\hat{}}{\tau} - d} \right)\sin\left( {\theta_{0} - \theta_{1}} \right)}}} \\{Q_{p} = {{\frac{1}{{Tf}_{s}}{\sum\limits_{n = 1}^{{Tf}_{s}}{q_{p}(n)}}} \approx {{- {AR}}\left( \overset{\hat{}}{\tau} \right)\sin\left( {\theta_{0} - \theta_{1}} \right)}}}\end{matrix},$ where T represents an integration time, f_(s) representsa sampling rate, n represents a time point, A represents an amplitude ofthe intermediate-frequency signal x(n) input into the tracking loop,R(·) represents an autocorrelation function of the ranging codes,{circumflex over (τ)} represents a distance between the local punctualcode and a signal ranging code, d represents an interval of the rangingcodes, θ₀ represents an initial phase of a carrier of theintermediate-frequency signal x(n) input into the tracking loop; and θ₁represents an initial phase of a locally-generated carrier signal. 5.The multipath suppression method based on the steepest descent methodaccording to claim 1, wherein a equation of the ranging code offset inStep 4 is as follows:${{\overset{\hat{}}{\tau}}_{k + 1} = {{\overset{\hat{}}{\tau}}_{k} - {\mu\frac{{P{F\left( {{\overset{¯}{S}}_{E}❘_{k}} \right)}} - {P{F\left( {{\overset{¯}{S}}_{P}❘_{k}} \right)}}}{d}}}},$or the equation is as follows:${{\overset{\hat{}}{\tau}}_{k + 1} = {{\overset{\hat{}}{\tau}}_{k} - {\mu\frac{{P{F\left( {{\overset{¯}{S}}_{P}❘_{k}} \right)}} - {P{F\left( {{\overset{¯}{S}}_{L}❘_{k}} \right)}}}{d}}}},$where {circumflex over (τ)}_(k+1), and {circumflex over (τ)}_(k)respectively represent {circumflex over (τ)} at a time point k+1 and atime point k, {circumflex over (τ)} represents a distance between thelocal punctual code and a signal ranging code, an interval between thetime point k+1 and the time point k is an integration time, μ is apositive scalar named step length, PF(·) represents a cost function, S_(E)|_(K) S _(P)|_(K) and S _(L)|_(K) respectively represent values of S_(E), S _(P), and S _(L) at the time point k, S _(E) represents anormalized value of S_(E), S _(P) represents a normalized value ofS_(P), S _(L) represents a normalized value of S_(L), andS _(E)=√{square root over (I _(E) ² +Q _(E) ²)},S _(P)=√{square rootover (I _(P) ² +Q _(P) ²)},S _(L)=√{square root over (I _(L) ² +Q _(L)²)}.